1. ## Limits

What does the function f(x)=1-2^(-x) approach as x goes to infinity?

2. Originally Posted by lilikoipssn
What does the function f(x)=1-2^(-x) approach as x goes to infinity?
$\displaystyle \lim_{x\to\infty}[1-2^{-x}]$

Using our laws of limits and algebra we rewrite this as

$\displaystyle \lim_{x\to\infty}1-\lim_{x\to\infty}\frac{1}{2^{x}}$

and we get $\displaystyle 1-\frac{1}{2^{\infty}}=1-0=1$

3. Originally Posted by Mathstud28

and we get $\displaystyle 1-\frac{1}{2^{\infty}}=1-0=1$
You'd better write $\displaystyle 1-\lim_{x \to \infty} \frac{1}{2^x}$

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4. Originally Posted by Moo
You'd better write $\displaystyle 1-\lim_{x \to \infty} \frac{1}{2^x}$

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I was trying to be practical opossed to formal...I dont do things like that...but when showing how to do something instead of just saying $\displaystyle \lim_{x\to\infty}\frac{1}{2^{x}}=0$ I like to show WHY it is
...it is just my preference...but you are correct in that it is informal and not to be done on tests

5. Originally Posted by Mathstud28
...it is just my preference...but you are correct in that it is informal and not to be done on tests
Just my opinion :
I think it's not very wise to act this way.. People could say in a test "but someone wrote this ! so I can !"
And that is the problem, it's your preference, but we're talking about an other one's exercise..